A dual approach to continuous-time envelope-constrained filter design via orthonormal filters

The envelope-constrained (EC) filtering problem was initially posed in the continuous-time domain as a constrained L² space optimization problem. However, only the discretized version has been solved, using various approaches. In this paper we consider the continuous-time EC filtering problem formulated using an orthonormal basis defined on a Hubert vector space. Carathéodory's theorem and the dual parametrization method are used to obtain a dual finite-dimensional optimization problem. Two iterative algorithms based on the gradient flow technique are then developed for solving this dual problem. The design of an EC optimal equalization filter for a communication channel is solved to illustrate the effectiveness of the proposed algorithm.